Consider a composite atom P described by a repetitive chain of historically ordered space-time events

$\Psi \left( \bar{r}, t \right) ^{\sf{P}} = \left( \sf{\Omega}_{1}, \sf{\Omega}_{2} \ldots \, \sf{\Omega}_{\it{i}} \, \ldots \, \sf{\Omega}_{\it{f}} \, \ldots \right)$

where each event $\sf{\Omega}$ is also characterized by its velocity $\overline{\sf{v}}$ and time of occurrence $t$. Changes between some arbitrary initial and final events are noted by

$\Delta \overline{\sf{v}} = \overline{\sf{v}} _{\it{f}} - \overline{\sf{v}} _{\it{i}}$

$\Delta t = t_{\it{f}} - t_{\it{i}}$

Definition: the **acceleration** vector is an ordered set of three numbers

$\bar{a} \equiv \Delta \overline{\sf{v}} / \Delta t$

The acceleration is used to describe changes in the trajectory of P. It can be experimentally determined by measuring the velocity and measurements of elapsed time. The norm of the acceleration is written without an overline

$a \equiv \left\| \, \bar{a} \, \right\|$